Let k be a field. We prove that any polynomial ring over k is a Kadison algebra if and only if k is infinite. Moreover, we present some new examples of Kadison algebras and examples of algebras which are not Kadison algebras.
2000 Mathematics Subject Classification: Primary 46H05, 46H20; Secondary 46M20.Every unital "combinatorially regular" commutative uniform complete locally m-convex algebra is local.
It is a survey talk concerning locally bounded algebras.
We define locally convex spaces LW and HW consisting of measurable and holomorphic functions in the unit ball, respectively, with the topology given by a family of weighted-sup seminorms. We prove that the Bergman projection is a continuous map from LW onto HW. These are the smallest spaces having this property. We investigate the topological and algebraic properties of HW.
Let A be an algebra over the field of complex numbers with a (Hausdorff) topology given by a family Q = {qλ|λ ∈ Λ} of square preserving rλ-homogeneous seminorms (rλ ∈ (0, 1]). We shall show that (A, T(Q)) is a locally m-convex algebra. Furthermore we shall show that A is commutative.
Let be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If has the (iii)-property, then its completion is an order-complete locally solid lattice group. (2) If is order-complete and has the Fatou property, then the order intervals of are -complete. (3) If has the Fatou property, then is order-dense in and has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on...
The present paper is a contribution to fill in a gap existing between the theory of topological vector spaces and that of topological abelian groups. Topological vector spaces have been extensively studied as part of Functional Analysis. It is natural to expect that some important and elegant theorems about topological vector spaces may have analogous versions for abelian topological groups. The main obstruction to get such versions is probably the lack of the notion of convexity in the framework...
We prove that every map T between two F*-spaces which preserves equality of distance and satisfies T(0) = 0 is linear.